Number Theory

    

Three Conjectures on the Numbers 6pq+1 Where P and Q Primes and Q=2p-1

Authors: Marius Coman

In this paper I make the following three conjectures on the numbers of the form n = 6*p*q + 1, where p and q are primes and q = 2*p – 1: (I) There exist an infinity of n primes; (II) There exist an infinity of n semiprimes; (III) There exist an infinity of n composites with three or more prime factors, 7 being one of them. Note that for all the first 46 pairs of primes [p, q] with the property mentioned (see the sequence A005382 in OEIS for these primes) the number n obtained belongs to one of the three sequences considered by the three conjectures above.

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[v1] 2016-03-03 10:23:06

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